738 IEEE Tansactins n Ultasnics, Feelectics, and Fequency Cntl, vl. 59, n. 4, Apil 0 Vltage-Cntlled Duble-Resnance Quatz Oscillat Using Vaiable-Capacitance Dide Ruzaini Izyan Binti Ruslan, Tmi Sath, and Tetsuya Akitsu, Membe, IEEE Abstact In this wk, we pesent a vaiable-fequency quatz cystal scillat that is able t scillate at LC esnance unde fequency lcking f a quatz cystal esnance, with the fequency tuning ealized by vaiable-capacitance dides. This cicuit shws a steep tansitin between LC scillatin mdes t quatz cystal duble-esnance, which shws a chaacteistic change in the scillatin fequency. Cntl vltage f this dide is pecisely adjusted fm the lw side t highe values and cnvesely in the vicinity f the scillatin mde tansitin. The tansitin f the scillatin mdes is expeimentally demnstated and cmpaed with an algebaic analysis. I. Intductin The piezelectic quatz cystal esnat is an essential device in almst all mden multimedia telecmmunicatin and electnic equipment f its many applicatins. Thei applicatins have expanded with the ecent develpment f sens applicatins, as pweful tls in the accuate handling f the time and fequency bases and measuement, i.e., in piezelectic esnat senss such as quatz cystal mic-balances (QCMs) and SAW senss [], []. In sens applicatins, the change in the quatz cystal esnance fequency is measued. When the sens is immesed in liquid, excitatin f cntinuus scillatin becmes difficult because the incease in paallel capacitance educes the esnance cnditin. Theefe, lage negative capacitance in the duble-esnance scillat is necessay t satisfy the scillatin cnditin. In a pevius wk, we epted the design cncept f the duble-esnance quatz cystal scillat and its scillatin chaacteistics when immesed in a liquid medium [3]. In this wk, we ppse a mdificatin f the duble-esnance scillat cicuit with a vaiable capacitance dide t geneate accuate fequency that can be adjusted pecisely t the taget fequency by the cntl vltage. The fequency stability f the tansitin fm LC esnance scillatin t the fequency lcking f quatz cystal scillatin is descibed. The standad f fequency stability is based n vaiance f discete multiple measues detemined by J. A. Banes et al. [4], D. W. Allan [5], and J. A. Manuscipt eceived Septembe 5, 0; accepted Decembe, 0. R. Izyan Binti Ruslan is with the Intedisciplinay Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi, Kfu, Japan. T. Sath is with the Pst Gaduate Pgam in the Intedisciplinay Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi, Kfu, Japan. T. Akitsu is with the Intenatinal Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi, Kfu, Japan (e-mail: akitsu@ yamanashi.ac.jp). DOI: http://dx.di.g/0.09/tuffc.0.5 Banes [6]. The measues, in this cntext, ae cnsideed as vaiance aund the mean f the multiple fequency measuement. The vltage-cntlled scillat must exhibit a lw phase nise t ensue sensitivity f sens applicatins, and t meet adjacent-channel and blcking equiements f telecmmunicatins. II. Analysis In this sectin, we descibe the design and analysis f the quatz cystal scillat with a vaiable-capacitance dide and cntl cicuit aimed t eplace the paallel capacitance f the iginal scillat cicuit. In additin t having lage negative esistance, the duble-esnant cicuit is used t incease the scillatin fequency s sensitivity t the capacitance change, when it is necessay, t take int cnsideatin the eactance f the dide package [7], [8]. A. Analysis f the Duble-Resnance Quatz Cystal Oscillat Fig. shws a cicuit diagam f the duble-esnance quatz cystal scillat (DRXO) discussed in Sath et al. [9]. This cicuit cnsists f an invete equivalent t a pai f CMOS FETs and tw inducts, L and L 3, necessay f the geneatin f lage negative esistance. Oiginally, the tuning f fequency was achieved by changing the individual capacitance C x inseted in paallel t the quatz esnat, whee the esnance cnditin is detemined by C x and the inducts. At a fequency in the vicinity f the esnance fequency f the quatz esnat, a cupled esnance mde is established. In Fig., the equivalent cicuit f the DRXO is shwn in pat. Fig. (a) shws the equivalent cicuit f the scillat when the LC scillatin mde ccus befe the fequency lcks. L c indicates the cmbined equivalent inducts f L and L 3. R c is the cmbined equivalent negative esistance f L, L 3, and the cnductance f invete IC f G m ; the paallel capacitance f quatz esnat C 0, tuning capacit C x, and stay capacitance C s ae cmbined in C 0x : C 0x = C x + C 0 + C s. Cnductance f FET g m is expessed with dain cuent I d and cnductance cefficient K defined in the tems f electn mbility and hle mbility, μ, and the unit gap capacitance, C g, whee W/L is the ati f width t length f the gate: G g g KI K C W m = m, m = d, = µ g. L 0885 300/$5.00 0 IEEE
uslan et al.: vltage-cntlled duble-esnance quatz scillat 739 Fig.. Cnfiguatins f simplified duble-esnance quatz cystal scillat: (a) LC scillatin mde and (b) quatz cystal scillatin with the mtin am. Fig.. Duble-esnance quatz cystal scillat and equivalent cicuit f the esnat: L and C ae seies inductance and seies capacitance detemining the seies esnance fequency, and C 0 is the paallel capacitance. The scillatin cnditin f this scillatin mde is defined as Rlc = R + Rc < 0, R = + 3, ω lc =, () LC c 0 x whee R is the intenal esistance f inducts L and L 3. In the case f the equivalent cicuit in Fig. (b), fequency is lcked when the fequency f the LC scillatin is clse t the fequency f the quatz cystal esnat. In the wds, the physical mtin am is epesented by R, L, and C in the equivalent cicuit f the quatz cystal esnat (C 0 is excluded), which tansfes the LC scillatin t the quatz esnance mde. L dci and R dci ae equivalent eactance f inductance and esistance, espectively. L c and R c in the LC scillatin in Fig. (a) ae cmbined with C 0 and C x. The scillatin cnditin f the quatz esnance mde is expessed as Rxt = R + Rdci < 0, ω xt =. () ( L + L ) C dci B. Develpment f the Vltage-Cntlled Duble-Resnance Quatz Cystal Oscillat Cicuit Fig. 3(a) shws a cicuit diagam f the vltage-cntlled duble-esnance quatz cystal scillat (VC DRXO), in which the tuning capacit C x in the iginal cicuit shwn in Fig. is eplaced with a vaiable-capacitance dide and dive cicuit. Fig. 3(b) shws a cicuit diagam f the VC DRXO with tw vaiable-capacitance dides. Bth dive cicuits include a lw-pass filte cnsisting f a few capacits and esists, allwing diect cuent t flw and t pevent paasitic bias vltage fm the ci- Fig. 3. The develped vltage-cntlled duble-esnance quatz cystal scillat cicuit: Cicuit cnstants: pass capacits: C = 0 µf, C 3, C 4, C 8, C 9, and C 0 = 000 pf, C 6 = 0 pf, C 7 = 0. µf; L and L 3 =.7 µh; R 4 and R 5 = 00 Ω; R 6, R 7, and R 8 = MΩ. Vaiable-capacitance dide C x, and C x : SV49B, CMOS Invete IC : TC7SHU04. (a) VC DRXO with the single vaiable-capacitance dide cntl system, (b) VC DRXO with the duble vaiable-capacitance dide cntl system.
740 IEEE Tansactins n Ultasnics, Feelectics, and Fequency Cntl, vl. 59, n. 4, Apil 0 cuit itself. R 4 and R 5 ae inseted at the invete s pwe input and the gund cupling t ptimize the gain f the invete thugh the negative feedback and pwe cnsumptin. The vaiable-capacitance dide peates in a eveseplaized bias, whee capacitances vay pptinally with the ecipcal f the length f the depletin laye. The depletin egin inceases when highe bias vltage is applied. The capacitance at a given bias is detemined fm C x c j0 = x = V Γ ( d ), ωcq, (3) x d φ 0 whee C j0 is the junctin capacitance at ze bias vltage, V d is the evese bias vltage applied, ϕ 0 is the built-in ptential baie f the dide, and Γ is the tuning slpe. Fig. 4 shws the schematic symbl and an equivalent cicuit f this cicuit cmpnent. Intenal esistance f the dide, x, is fund fm capacitance C x and quality fact Q d, as defined as in (3). Changing the cntl vltage, the esnant fequency vaies fm quatz cystal esnance t LC esnance cntinuusly. The cnstants in this elatin wee detemined by cmpaing the cntl vltage t the vaiable-capacitance dides with knwn capacitance C. C xeal is the measued capacitance. The fllwing paametes expess the mst pbable appximatin: f the duble-dide system, C j0 = 600 pf, ϕ 0 =.0, and Γ =.5, and f the single-dide system, C j0 = 400 pf, ϕ 0 =.0, and Γ =.7, as in Fig. 4(c). In the scillat cicuit, the capacitance in the singledide system becmes less than twice that in the dubledide system because the leakage cuent influences the capacitance. In the expeimental esult, sme discepancy in the cntl chaacteistics is fund, caused by this influence f the leakage cuent n the cntl vltage, in the single-dide system. Because the diffeence between the active cicuit f the develped scillat cicuit and the iginal duble-esnance cicuit is negligible except f the eplacement with the vaiable-capacitance dide and the additinal dive cicuit, the scillatin cnditin and the fequency cnditin can be detemined in a simila manne. Natually, the scillatin cnditins ae the same as () and () f bth mdes. The iginal cicuit in Fig. is cnveted t equivalent cicuit, shwn in Fig. 5(a). G M is the feedback cnductance f invete IC, defined in Gm ωl ωl3 GM =, = = +, 3, (4) G R Q Q m f 3 whee the feed-back esists R f is equal t R 4 and R 5 in Fig 3. G m is the pen-lp cnductance. The intenal esistances f inducts and 3 ae detemined by the quality fact Q, as shwn in (4). Induct L 3, utput capacitance, and stay capacitance f the cicuit ae cmbined int the impedance Z 3t. The eal pat and imaginay pats 3 and L 3t ae fund: 3t = ω ( ) + ( ) ( L3t = L3 ) ( ) ω 3 ω ω ω3 ω ω ω ω 3 ω ω ω ω 3 ( ) + ( ) (5) (6) =, ω3 =. (7) LC C 3 Kichhff s law is applied t the cicuit diagam in Fig. 5(a). The equatin f nde vltage V g and flwing cuents alng Z, Z, and Z 3t ae fund: 3 Fig. 4. Schematic symbl and equivalent cicuit f the vaiable-capacitance dide [7], [8]. Filled cicles: Single-dide cntl system shwn in Fig. 3(a). Open cicles: duble-dide cntl system shwn in Fig. 3(b). Cicuit cnstants: L and L 3 =.7 μh; C d and C d SV49B. (a) Schematic symbl, (b) equivalent cicuit, and (c) vltage-capacitance cuve f the duble vaiable-capacitance dide cntl system. Vg = Z i (8) + GMZ 0 3 i = 3 ZZ Z i 0. t (9) The elatin between cuent vects i and i 3 ae defined as i = ( + G Z ) i (0) 3 M
uslan et al.: vltage-cntlled duble-esnance quatz scillat 74 L ω ω ω c ( ) ( ) ω ω c Lc ω ω ( ) + ( ) ω ω c (6) =, ωc =. C0xRc LC c 0 x (7) dci = Because the same scillatin cnditins ae applicable, the cicuit in Fig. 5(b) can be simplified int Figs. (a) and (b) f bth quatz cystal scillatin and LC scillatin mdes. III. Expeimental Results and Cmpaisn With Analysis Fig. 5. Simplified equivalent cicuits f the duble-esnance quatz cystal scillat cicuit: (a) equivalent cicuit and (b) equivalent cicuit. ( Z + Z ) i + Z i =. () 3t 3 0 The lp cicuit f impedances f Z, Z, and Z 3t can be expessed as a nmal equatin: Z + Z + Z + G ZZ =. () 3t M 3t 0 Refeing t cicuit equatin (9), the eal and imaginay pats f the cmbined impedances f the active cicuit excluding Z, ae shwn in Fig. 5(b). Each pat is fund as M 3t 3 t 3 t R = G ( ω L L ), R = + (3) c Lc = L( + GM3t) + L3t( + GM), (4) whee the eactance is inductive. Fm Fig. 5(b), C 0, C x, and C s ae cmbined with R c and L c, and cmbined eactance L dci and esistance R dci ae fund, whee R dci < 0: R dci = Rc ω ω ( ) + ( ω ) ωc (5) In the fist pat f the expeiment, the capacitance-vltage chaacteistics f the vaiable-capacitance dide wee veified. Fequency shift in a single vaiable-capacitance dide shws diffeent chaacteistics in inceasing and descending cntl vltage. The duble vaiable-capacitance dides system exhibits simila fequency shift whethe in inceasing descending cntl vltage, as shwn in Figs. 6 and 7. In this expeiment, the fequency was measued t digits with a univesal fequency cunte (Type 530A, Agilent Technlgies Inc., Santa Claa, CA) with an extenal time base (Rb-330N ubidium atmic scillat, Epsn-Tycm C. Ltd., Suwa, Japan). Tuning f cicuit paametes was pefmed in the fllwing way. Fist, a taget fequency was set by eplacing ceamic capacits manually and adjusting the bias vltage f the vaiable-capacitance dide. Afte the capacitance and vltage values wee cmpaed, a mde change fm LC scillatin t quatz cystal esnance was fund. In Fig. 6(a), while applying inceasing vltage scillatin, fequency was bseved fm highe t lwe values f capacitance. The fequency f LC scillatin inceased as the capacitance deceased befe the fequency is lcked by the quatz cystal esnance fequency. The scillatin is unlcked and finally jumps t the LC esnance mde. Then, deceasing the applied vltage, the capacitance is vaied fm lwe t highe capacitance. The capacitance shifts in incemental steps at highe vltage, causing the LC scillatin t emain until the dide is chaged t appximately 45 pf, in the same egin whee the fequency is lcked with inceasing cntl vltage. The capacitance ange f the quatz cystal esnance is ten times wide than the ascending cntl. Fig. 6(b) shws the dependence f negative esistances n capacitance C x, f bth inceasing and deceasing cntl vltage; the fequency lcking stats at the maximum negative esistance R dci, appximately 0 kω. At this pint, the fequency f the LC scillatin f lc is equal t the quatz cystal esnance fequency f xt. The quatz cystal esnance cntinues t 8 pf in the inceasing cntl and 38 pf in the deceasing cntl. The mde tansfe f LC scillatin t quatz cystal esnance was bseved at the same fequency.
74 IEEE Tansactins n Ultasnics, Feelectics, and Fequency Cntl, vl. 59, n. 4, Apil 0 Fig. 6. Fequency jump and abslute value f fequency deviatin in the vaiable-capacitance dide vltage-cntlled scillat cicuit: (a) Fequency jump and the fequency deviatin. Filled squaes: fequency shift with ascending bias vltage, f vd ( ). Open squaes: fequency shift with descending bias vltage, f vd ( ). Filled cicles: abslute value f nmalized deviatin f f vd ( ), Δf vd ( )/f. Open cicles: abslute value f nmalized deviatin f f vd ( ), Δf vd ( )/f. (b) Oscillatin fequency and the equivalent negative esistance with the single vaiable-capacitance dide system. Open squaes: scillatin fequency f inceasing cntl vltage. Filled squaes: deceasing cntl vltage. Bken line: the equivalent negative esistance as a functin f C x. Fig. 7. Fequency shift and abslute value f fequency deviatin in the duble vaiable-capacitance dide cicuit: (a) Fequency shift and the fequency deviatin. Filled squaes: fequency shift f vd. Open squaes: abslute value f nmalized deviatin f f vd, Δf vd /f. (b) Oscillatin fequency f descending bias vltage, nmalized fequency shift, and equivalent negative esistance as a functin f C x. Cicuit cnstants in bth cicuits: L and L 3 =.7 µh; Q and Q 3 = 00; utput capacitance C = 0 pf; G M = 0 ma/v. Equivalent cicuit cnstant f the quatz cystal esnat: paallel capacitance C 0 = 5. pf; L =.7 mh; C = 4.6 pf; R = 4.5 Ω; f = 8.9989 MHz. In the case f the duble vaiable-capacitance dide cntl system, fequency shifts in the same way f ascending and descending cntl. Fig. 7(a) shws a fequency lcking at the fequency f quatz cystal esnance. The scillatin mde tansfes t the LC scillatin in the highe-capacitance egin, and the deviatin f fequency shws a step-wise change f appximately 0 ppm. In Fig. 7(b), the scillatin mdes tansfe at the same fequency and negative esistance as in Fig. 6(b). Because appximately twice the applied vltage is necessay t shw the same capacitance ange as the single-dide system, and the scillatin is stabilized and satuated when enteing the egin f quatz cystal esnance, the gain in the scillatin was smalle cmpaed with the singledide system because f deceasing capacitance even at the same vltage, which caused the scillatin t emain in the quatz cystal esnance mde unless the negative esistance eaches the maximum value. Fig. 8 cmpaes the fequency dependence n the bias vltage f single and duble vaiable-capacitance dide cntl systems f the develped scillat. The cefficient f deteminatin R is the linea tendline in which pltted data ae mst eliable when its value is equal t unity, whee R is defined as the ati f the sum f the esidual squaes, SS egessin, t SS ttal. The initiatin f the quatz cystal esnance scillatin is in-
uslan et al.: vltage-cntlled duble-esnance quatz scillat 743 y n fn fn fi = =, whee yi =, fi = fi f0. f0 f0 f0 (9) Allan vaiance f a finite numbe f samples is defined as M ( yn+ yn) σy( ) M n= ( f f ) + + ( fm f = M f0 M ). (0) Fig. 8. Jump f the scillatin mde and the lineaity f bias vltage vesus fequency. (a) Lineaity f the single vaiable-capacitance dide cntl system. (b) Lineaity f the duble vaiable-capacitance dide cntl system. Fig. 9 shws the aveaged Allan vaiance f inceasing and deceasing bias vltage. Deceasing the cntl vltage, the Allan vaiance steps dwn t.0 0 0 at.83 V (C x = 35 pf), and anges t.9 0 9, at the inceasing bias vltage at 5.9 V (C x = 56 pf). In bth cntl systems, the stability is highe than the LC scillatin mde, shwing high stability with appximately 0 9 in the whle ange in which the influence f the quatz cystal esnance lasts. Fm this esult, we can say that the duble vaiablecapacitance dide cntl system in the VC DRXO shws gd lineaity f bias vltage and fequency scillatin with easnable sht-tem stability in the quatz esnance mde. This scillat cicuit als pvides wide tuning fequency ange ve LC scillatin lcked by quatz cystal esnance and the LC scillatin unlcked mde. Fig. 0 cmpaes the VC DRXO and the VC LCO, bth using the vaiable-capacit dide cntl system f which nly the esnance fequency belw the seies esnance is shwn. The VC DRXO is successfully peated dicated at the quatz cystal esnance that causes the sudden geneatin f the mtin am at the LC scillatin equal t the esnance fequency. Then, a hysteesis f the scillatin mde is bseved in the cntl chaacteistics. The lck f the scillatin mde can be explained by cnsideing the decease in gain in the statinay scillatin satuated, which is insufficient f the excitatin f the LC scillatin. Next, the sht-tem stability f the scillat was evaluated using Allan vaiance. The scillatin fequency f n is sampled at the inteval ; n is the sequential numbe. The scillatin fequency is given by the esnance fequency f 0 and the fequency deviatin f n : fn = f 0 + fn. (8) Nmalized fequency-shift is defined as Fig. 9. Allan vaiance f vaius values f C x. Open squaes: LC scillatin f inceasing bias vltage. Filled squaes: LC scillatin f deceasing bias vltage. Open cicles: quatz cystal esnance f inceasing bias vltage. Filled cicles: quatz cystal esnance f deceasing bias vltage.
744 IEEE Tansactins n Ultasnics, Feelectics, and Fequency Cntl, vl. 59, n. 4, Apil 0 Fig. 0. Sht-tem stability dependence n fequency deviatin. Open cicles: σ f LC scillatin in LC scillat mde. Open squaes: σ f LC esnance and quatz cystal esnance in the duble-esnance scillat. in a wide fequency ange, maintaining highe stability in the same egin as the iginal LC scillat. IV. Cnclusin In this wk, we descibed the cncept f fequency cntl using vaiable-capacitance dides in the DRXO. The cntl system cicuit shwed significant diffeences in the effect f the capacitance, negative esistance f the active cicuit t geneate the quatz cystal scillatin, and stability. In the cmpaisn with the cnventinal Piece scillat, the DRXO with the vaiable-capacitance dide cntl system shwed the fllwing: ) The influence f the paallel capacitance f the quatz cystal esnat can be suppessed. This featue enables, f example, scillatin in a liquid medium. ) Reactance f the active cicuit peates in the negative eactance egin, esulting in a lage negative esistance. 3) The VC DRXO shws a vaiety f the scillatin mde in which the scillatin fequency cntinuusly vaies fm the LC scillatins t the quatz cystal esnance. This mde change clealy shws the fundamental pblem f the quatz cystal esnance. With this featue, this scillat cicuit can be an expeimental taget t study the influence f cicuit eactance and the basic cncept f stability, the fundamental elatin between paallel capacitance and the mtin am, and the pssibility f scillatin unde the seies esnance fequency. Fm expeimental esults, the develped diving cicuit used in this wk that indicated a high abslute value Fig.. Equivalent cicuit f the vaiable-capacitance dide. (a) Vaiable capacitance dide in the seies cnfiguatin. (b) Vaiable-capacitance dide in the paallel cnfiguatin. f negative esistance up t 0 kω, we can say the develped cicuit is suitable f use in QCM applicatins even in a liquid medium. This cntl system can demnstate inteesting tuning and detuning f the duble esnance and the fequency jump. Stability f the scillatin fequency is maintained even in the case in which a hysteesis f the cntl vltage was bseved. The Allan vaiance σ f the lcked fequency shwed a maximum value f sht-tem stability at 0 9. In this wk, the hysteesis was suppessed by the duble-dide cntl system that allws fine tuning in nawe ange. Althugh the vaiable-capacitance dide is widely used in quatz cystal scillat cicuits, such as in vltagecntlled scillats (VCOs) tuning systems, the cystal VCO that is claimed t be the mst stable scillat amng thes (i.e., LC VCO, multivibat VCO, etc.) is p in its lineaity and has a naw fequency tuning ange. Hweve, the applicatins in the field f piezelectic sensing have nt been widely expled. F the naw negative esistance egin in quatz esnance fequency that appeas in the analysis, mde selectin amng multiple mdes f quatz cystal esnats has significant ptential in sensing applicatins. A gd vltage-cntlled cystal scillat with high stability, gd lineaity, and a wide fequency tuning ange was als successfully demnstated. Appendix A Equivalent Cicuit f the Vaiable-Capacitance Dide F a vaiable-capacitance dide, tw equivalent cicuits ae pssible, depending n whethe intenal esistance is in seies paallel with the capacitance.
uslan et al.: vltage-cntlled duble-esnance quatz scillat 745 Fig. shws tw equivalent cicuit diagams f the vaiable-capacitance dide. In this case, f a high Q value, the equivalent cicuit is assumed t be a seies cnfiguatin f the depleted egin, which is almst pue capacitance, and the undepleted egin is almst a esist [7], [8]. At the pesent scillatin f 9 MHz and Q value f 00, a typical esult f the intenal esistance is 3 Ω at C x = 30 pf. Thus, the intenal esistance was neglected in the discussin. Acknwledgments [8] Applicatin Nte: Vaact Dides, Skywks Slutins Inc., Wbun, MA 008. [9] T. Sath, R. Izyan Ruslan, S. Gth, and T. Akitsu, Duble-esnance quatz cystal scillat and excitatin f a esnat immesed in liquid media, IEEE Tans. Ultasn. Feelect. Feq. Cntl, vl. 58, n. 4, pp. 788 797, 0. Ruzaini Izyan Binti Ruslan gaduated fm the Depatment f Electical Engineeing, Univesity f Yamanashi, in Mach 00. She is a Maste f Engineeing candidate in the Intedisciplinay Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi. He special inteest is in the piezelectic scillat and its applicatins. M. M. Maum is acknwledged f his kind advice and deteminatin f the equivalent cicuit cnstant f quatz cystal esnats. Refeences [] U. A. Beleka and S. A. Ladhake, High-pefmance vltagecntlled scillat (VCO) using 65 NM VLSI technlgy, Int. J. Cmp. Netw. Cmmun., vl., n. 4, pp. 73 8, 00. [] A. V. Gebennikv, Stability f negative esistance scillat cicuits, Int. J. Elect. Eng. Educ., vl. 36, pp. 4 54, 999. [3] T. Sath, R. Izyan Ruslan, Y. Katu, M. Maum, and T. Akitsu, Fu-segment scillatin cicuit f piezelectic sensing devices, IEEJ Tans. Elect. Electn. Eng., vl. 6, n. 3, pp. 80 86, 0. [4] J. A. Banes, A. R. Chi, L. S. Cutle, D. J. Healey, D. B. Leesn, T. E. McGunigal, J. A. Mullen J., W. L. Smith, R. L. Sydn, R. F. C. Vesst, and G. M. R. Winkle, Chaacteizatin f fequency stability, IEEE Tans. Instum. Meas., vl. IM-0, n., pp. 05 0, 97. [5] D. W. Allan, Statistics f atmic fequency standads, Pc. IEEE, vl. 54, n., pp. 30, 966. [6] J. A. Banes, Atmic time keeping and the statistics f pecisin signal geneats, Pc. IEEE, vl. 54, n., pp. 07 0, 966. [7] SV49B Datasheet: Vaiable Capacitance Dide (AM Radi Band Tuning Applicatins). Tshiba Semicnducts, Tky, Japan. Tmi Sath gaduated fm the Depatment f Electnics, Yamanashi Univesity, in Mach 97. He hlds a Dct f Medicine and Engineeing degee fm the Univesity f Yamanashi. He is cuently a lectue in chage f the pstgaduate pgam f the Intedisciplinay Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi. Tetsuya Akitsu gaduated fm the Depatment f Electnics, Kyt Univesity, in Mach 974. He hlds Maste f Engineeing and Dct f Engineeing degees fm Kyt Univesity. He is cuently a pfess in the Intedisciplinay Gaduate Schl f Medicine and Engineeing, Univesity f Yamanashi. He is a membe f IEEE and the Institute f Electical Engineeing f Japan (IEEJ).